Amid reports of deadlock and just a week after the group’s Democrats and Republicans released competing plans, the Joint Select Committee on Deficit Reduction convened for its fourth public policy hearing on Tuesday afternoon. On the docket: testimony from leaders of past deficit-reduction groups, including former Congressional Budget Office Director Alice Rivlin and former Sen. Alan Simpson, R-Wyo.

With just over three weeks until the deadline to present its final plan to Congress, the super committee has given little reason for hope. Simpson, who led the president’s fiscal commission last year with former White House Chief of Staff Erskine Bowles, and Rivlin, who put together a plan with former Sen. Pete Domenici, R-N.M., were summoned with their co-chairs to advise the committee on the best path forward to reach a bipartisan plan worth some $1.2 trillion to $1.5 trillion in deficit cuts over a decade.

The Simpson-Bowles and Rivlin-Domenici plans each achieved roughly $4 trillion in savings over that time period – through a mix of spending cuts and revenue increases – but the expectation that the super committee will “go big” is dwindling as the group plays out what feels like a sequel to this summer’s debt-ceiling fight.

Still, Tuesday brought reports that Republicans are softening on revenue and that six members of the committee are trying to broker a compromise that could achieve slightly more than the mandated $1.5 trillion in savings.

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The six super committee Republicans and their congressional leaders have thus far declined to consider any tax increases, including ending tax breaks, unless they were linked to broader tax reform. And the GOP has insisted that overhauling the tax code be revenue neutral—a guarantee they want written into law.

But GOP sources confirmed to National Journal that Republican leaders and members of the super committee may work to close some tax loopholes in a new proposal they will present to the deficit-reduction panel’s Democrats.

Republicans are willing to consider decoupling loophole closures from an overall tax-code rewrite, and any GOP offer would likely also task committees of jurisdiction with coming up with a revenue-neutral tax-reform plan, said GOP sources familiar with super committee deliberations. They declined to cite specific tax-code changes or their total value.

Spokesmen for House Speaker John Boehner, R-Ohio, and Senate Minority Leader Mitch McConnell, R-Ky., declined to comment on such a GOP plan.